Confined quantum systems: a comparison of the spectral properties of the two-electron quantum dot, the negative hydrogen ion and the helium atom

Abstract

The spectrum, the electron density distribution and the character of three two-electron quantum systems, namely the two-electron quantum dot, the negative hydrogen ion and the helium atom, confined by an anisotropic harmonic oscillator potential, have been studied for different confinement strengths, ω, by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set supplemented by a quantum chemical standard Cartesian Gaussian basis set, respectively, and a full CI wavefunction. Energy level diagrams and electron density distributions are displayed for low lying electronic singlet states and selected confinement parameters. The results for the three confined quantum systems are compared with each other: in general, the absolute energies of the states and the interval between states increase with increasing confinement, ω. The ordering of states may vary for different values of ω. The shape of the electron density distribution differs among the three systems. Its size increases in the order He < H− < two-electron quantum dot. Electron distributions in prolate type confinement are stretched along the z axis, while those in oblate type are compressed with respect to this axis. The CI wavefunction of most of the low lying states for the helium atom and the negative hydrogen ion is dominated by one configuration, while some of the CI wavefunctions corresponding to states of the two-electron quantum dot have more than one leading configuration. The ground state CI wavefunctions of the negative hydrogen ion and the helium atom confined in a spherical potential are dominated by harmonic oscillator functions up to 82.4 and 47.1%, respectively, for the smallest confinement of ω = 0.1. These values increase to 98.8 and 89.0%, respectively, for ω = 0.5.